Curvature of Fields of Quantum Hilbert Spaces

lempert, lászló; szo˝ ke, róbert;

We show that using the family of adapted Kähler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank 1, the field Hcorr of quantum Hilbert spaces produced by geometric quantization, including the half-form correction, is flat if M is the three-dimensional sphere and not even projectively flat otherwise.